function [INFavgL,SUPavgL,MEDavgL,INFavgH,SUPavgH,MEDavgH,IRFdraws_histL,IRFdraws_histH] = VARirbandtrue_endint1shock_historiesEnd2_futureN_L(VAR,OIRF_optavg,pick,perc,ndraws,pctg,typeImpulse,fast)
% =======================================================================
%
%this function compute GIRFs and bootstrapped confidence bands for the case when there
% are interaction terms between 2 endogenous variables, where one is
%considered as a "conditioning indicator" to construct two different states.
%
% =======================================================================
% [INFavgL,SUPavgL,MEDavgL,INFavgH,SUPavgH,MEDavgH,IRFdraws_histL,IRFdraws_histH] = VARirbandtrue_endint1shock_historiesEnd2_futureN(VAR,OIRF_optavg,pick,perc,ndraws,pctg,typeImpulse,fast)
% -----------------------------------------------------------------------
% INPUTS
%   VAR     : VAR results structure obtained with VARmodel by A. Cesa Bianchi
%	OIRF_optavg : options to compute the  GIRFs (is the output of VARirtrue_sim1shock_histories_futureN)
%   pick   : variable to be shocked (order as from Cholesky decomposition)
%   perc  :  percentile that separe the Low from the High state
%   ndraws    : number of draws for boostrapping
%   pctg      :  confidence level
%   typeImpulse : put  0 for a standard deviation shock , if 1 instead a 1
%                 unitary increase in the variable, if n a shock equal to n standard
%                 deviations is considered.
%   fast    : 1 to be fast (avoid estraction future shocks in obtaining the GIRF - is a fairly good approximation/ 0 to consider them
%
% OUTPUT
%   INFavgL(t,j,k) = lower confidence band (t steps, j variable, k shock)
%   for the Low state
%   SUPavgL(t,j,k) = upper confidence band (t steps, j variable, k shock)
%   for the  Low state
%   MEDavgL(t,j,k) = median response (t steps, j variable, k shock) for the
%   Low state
%   INFavgH(t,j,k) = lower confidence band (t steps, j variable, k shock)
%   for the High state
%   SUPavgH(t,j,k) = upper confidence band (t steps, j variable, k shock)
%   for the  High state
%   MEDavgH(t,j,k) = median response (t steps, j variable, k shock) for the
%   HIgh state
%   IRFdraws_histL(t,j,k,nhistL) = responses for each draw in the L
%   state
%   IRFdraws_histH(t,j,k,nhistL) = responses for each draw in the H
%   state
% =======================================================================
%
% by Giovanni Pellegrino
%           [developed having as starting point the function VARirband by
%           Ambrogio Cesa Bianchi]



%% Retrieve some parameters from the structure VAR and IRF_opt
%=============================================================

nsteps = OIRF_optavg.nsteps;
ordend = OIRF_optavg.ordend;
ordend2= OIRF_optavg.ordend2;

beta     = VAR.beta;  % rows are coefficients, columns are equations
nvars    = VAR.neqs;
nvar_ex  = VAR.nvar_ex;
nlags    = VAR.nlag;
c_case   = VAR.c_case;
nobs     = VAR.nobs;
Y        = VAR.Y;
resid    = VAR.residuals;
clear VAR

if pick~=ordend
    error('Error: pick must be equal to the variable used as ordend in the VAR.')
end

numExpl=0;

mode =OIRF_optavg.mode;
draws=OIRF_optavg.draws;

IRFdraws_histL=NaN(nsteps,nvars,nvars,ndraws); 
IRFdraws_histH=NaN(nsteps,nvars,nvars,ndraws); 


%% Create the matrices for the loop
%==================================


%% Loop over the number of draws, generate data, estimate the var and then
%% calculate impulse response functions
%==========================================================================
tt = 1; %cycle over draws
while tt<=ndraws
    disp(['Loop ' num2str(tt) ' / ' num2str(ndraws) ' draws'])
    
    %% STEP 1: use the Bootstrap method to generate the residuals
    
    y_artificial = zeros(nobs,nvars);
    
          % Use the residuals to bootstrap: generate a random number bounded
        % between 0 and # of residuals, then use the ceil function to select
        % that row of the residuals (this is equivalent to sampling with replacement)
        u = resid(ceil(size(resid,1)*rand(nobs,1)),:);

    
    %%
    
    %%IMPORTANT:
    % to have the right results when there are interactions between
    % endogenous variables one has to construct properly also the
    % series for the interaction variables from each draw. It is important because the
    % interaction variables have to respect the link that they have
    % with our chosen endogenous variables.
    exog_draw=zeros(nobs,nvar_ex);
    
    %% STEP 2: generate the artifcial data
    
    %% STEP 2.1: initial values for the artificial data
    % Intialize the first nlags observations with real data + plus artificial
    % residuals. Nonetheless, in the estimation of the VAR on the simulated data,
    % I through away the first nobs observations so it should not matter.
    
    LAG=[];
    
        ii=1;
    
    for jj = 1:nlags
        y_artificial(jj,:) = Y(ii+jj-1,:) + u(jj,:);
        LAG = [y_artificial(jj,:) LAG];
        % Initialize the artificial series and the LAGplus vector
        if c_case==0
            LAGplus =          LAG;
        elseif c_case==1
            LAGplus = [1       LAG];
        elseif c_case==2
            T = (1:nobs)';
            LAGplus = [1 T(jj) LAG] ;
        end
    end
    
    
    if nvar_ex~=0 % to contruct the interaction variables
        if nlags==1
            LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend)];
        elseif nlags==2
            LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars)];
        elseif nlags==3
            LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars)];
        elseif nlags==4
            LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars) LAG(1,ordend2+3*nvars)*LAG(1,ordend+3*nvars)];
        elseif nlags==5    
            LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars) LAG(1,ordend2+3*nvars)*LAG(1,ordend+3*nvars) LAG(1,ordend2+4*nvars)*LAG(1,ordend+4*nvars)];
        else disp('Error: for now it is possible only to have nlags up to 5.')
        end
    end
    
    
    
    
    %% STEP 2.2: generate artificial series
    % From observation nlags+1 to nobs, compute the artificial data
    for jj = nlags+1:nobs
        
        for mm = 1:nvars
            % Compute the value for time=jj
            y_artificial(jj,mm) = LAGplus * beta(1:end,mm) + u(jj,mm);
        end
        % now update the LAG matrix
        LAG = [y_artificial(jj,:) LAG(1,1:(nlags-1)*nvars)];
        if c_case==1
            LAGplus = [1 LAG];
        elseif c_case==2
            LAGplus = [1 T(jj) LAG];
        end
        
        if nvar_ex~=0 % to construct properly also the interaction variables
            if nlags==1
                LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend)];
            elseif nlags==2
                LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars)];
            elseif nlags==3
                LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars)];
            elseif nlags==4
                LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars) LAG(1,ordend2+3*nvars)*LAG(1,ordend+3*nvars)];
            elseif nlags==5
                LAGplus = [LAGplus LAG(1,ordend2)*LAG(1,ordend) LAG(1,ordend2+nvars)*LAG(1,ordend+nvars) LAG(1,ordend2+2*nvars)*LAG(1,ordend+2*nvars) LAG(1,ordend2+3*nvars)*LAG(1,ordend+3*nvars) LAG(1,ordend2+4*nvars)*LAG(1,ordend+4*nvars)];
            else disp('Error: for now it is possible only to set nlags up to 5.')
            end
            
        end
    end
    

    numb=isnan(y_artificial(nobs,ordend));
    if numb~=1    % if one bootstrap draw delivers an explosive series for the endogenous
    % variable the draw is repeated with a new sequence of drawn residuals
        
        
        % sometimes, however, the artificial sample although divergirg,
        % still doesn't take NaN values for the number of iterations considered. In
        % these cases the final simulated observations take extreme values with
        % respect to initial values, so that to give problems in the
        % VAR estimation step. Hence the bootstrap draw necessitates to be repeated. 
        % Instead than using an arbitrary criterion, we discard just the
        % draws giving problems in the VARmodel estimation function. In
        % particular: i) we repeat the draw if errors or specific warning
        % and ii) repeat the draw if all histories are discarded.
        
        warning('error', 'MATLAB:nearlySingularMatrix'); % turn this specific warning into an error. 
        try 
            %% STEP 3: estimate VAR on artificial data.
            
            % here, after having simulated a series for the endogneous
            % variables, we also obtain the corresponding simulated series
            % for the interaction variables
            if nvar_ex~=0
                for ii=nlags+1:nobs
                    if nlags==1
                        exog_draw(ii,:)=y_artificial(ii-1,ordend2)*y_artificial(ii-1,ordend);
                    elseif nlags==2
                        exog_draw(ii,:)=[y_artificial(ii-1,ordend2)*y_artificial(ii-1,ordend) y_artificial(ii-2,ordend2)*y_artificial(ii-2,ordend)];
                    elseif nlags==3
                        exog_draw(ii,:)=[y_artificial(ii-1,ordend2)*y_artificial(ii-1,ordend) y_artificial(ii-2,ordend2)*y_artificial(ii-2,ordend) y_artificial(ii-3,ordend2)*y_artificial(ii-3,ordend)];
                    elseif nlags==4
                        exog_draw(ii,:)=[y_artificial(ii-1,ordend2)*y_artificial(ii-1,ordend) y_artificial(ii-2,ordend2)*y_artificial(ii-2,ordend) y_artificial(ii-3,ordend2)*y_artificial(ii-3,ordend) y_artificial(ii-4,ordend2)*y_artificial(ii-4,ordend)];
                    elseif nlags==5
                        exog_draw(ii,:)=[y_artificial(ii-1,ordend2)*y_artificial(ii-1,ordend) y_artificial(ii-2,ordend2)*y_artificial(ii-2,ordend) y_artificial(ii-3,ordend2)*y_artificial(ii-3,ordend) y_artificial(ii-4,ordend2)*y_artificial(ii-4,ordend) y_artificial(ii-5,ordend2)*y_artificial(ii-5,ordend)];    
                    end
                end
                
                %
                
                VAR_draw = VARmodel(y_artificial(nlags+1:end,:),nlags,c_case,exog_draw(nlags+1:end,:));% the first observaation are not considered
                
                Sigma    = VAR_draw.sigma;
                [Cho, chol_flag] = chol(Sigma);
                S = Cho';
                if chol_flag~=0
                    disp('-------------------------------------');
                    disp('Error: VCV is not positive definite');
                end
                residStruct=(S\VAR_draw.residuals')'; clear S Cho Chol_flag
                
            else
                VAR_draw = VARmodel(y_artificial(1:end,:),nlags,c_case);
            end
            
            
            %% STEP 4: calculate "ndraws" impulse responses and store them
            
            if nvar_ex~=0
%                 %algoritm to select all histories for the Low and High state:
%                 %---------------------------------------------------------%
%                 %-------------- Replace Relevant code here BEG------------%
%                 %---------------------------------------------------------%
                percL=10;
                toler=5;  %tolerance threshold
                jj1=0; %starting value for jj (Low  histories, 1 shock)
                jj2=0; %starting value for jj (Low  histories, 2 shocks)
                U_draw=VAR_draw.X(:,c_case+pick);
                %-------------------------------------------------------------------------%
                thrL1=prctile(y_artificial(nlags+1:end,ordend2),percL-toler);
                thrL2=prctile(y_artificial(nlags+1:end,ordend2),percL+toler);
%                 if SelectOnPastVolaOrPastShocks    
                %algoritm to select all histories for low and high uncertainty
                %using tolerance regions, find threshold
%                 %selecting histories based on volatility level:
%                 for ii=1:VAR_draw.nobs
%                     observ=VAR_draw.X(ii,c_case+ordend2);
%                     
%                     if observ<=thrL2 && observ>=thrL1  %  5th perc. < Unc <15th perc
%                         if     U_draw(ii,1) < mean(U_draw)-0.5*std(U_draw)
%                             jj1=jj1+1;
%                             historiesL(jj1,:)=VAR_draw.X(ii,:);
%                         elseif U_draw(ii,1) > mean(U_draw)+0.5*std(U_draw)
%                             jj2=jj2+1;
%                             historiesH(jj2,:)=VAR_draw.X(ii,:);
%                         end
%                     end
%                 end
%                 else
%                 %selecting histories based on previous shock being positive or negative:
                indexL  =[find(VAR_draw.X(:,c_case+ordend2)<=thrL2 & VAR_draw.X(:,c_case+ordend2)>=thrL1)]; indexL = setdiff(indexL,1);
                %[repmat(thrL1,length(indexL),1) VAR.X(indexL,c_case+ordend2) repmat(thrL2,length(indexL),1)]
                indexLL = indexL(find(residStruct(indexL-1,pick)<-0.5)); %< 25th perc
                indexLH = indexL(find(residStruct(indexL-1,pick)> 0.5)); %> 75th perc
                historiesL = VAR_draw.X(indexLL,:);
                historiesH = VAR_draw.X(indexLH,:);
%                 end
%                 %---------------------------------------------------------%
%                 %-------------- Replace Relevant code here BEG------------%
%                 %---------------------------------------------------------%
                  %--------------------  GDP detrended -------------------%
                thrL2=prctile(y_artificial(nlags+1:end,ordend2),15);
%  
% %                 %algoritm to select all histories for low and high uncertainty
% %                 %using tolerance regions, find threshold
% %                 for ii=1:VAR_draw.nobs
% %                     observ=VAR_draw.X(ii,c_case+ordend2);
% %                     
% %                     if observ<=thrL2 %  <15th perc
% %                         if     U_draw(ii,1) < mean(U_draw)-0.5*std(U_draw)
% %                             jj1=jj1+1;
% %                             historiesL(jj1,:)=VAR_draw.X(ii,:);
% %                         elseif U_draw(ii,1) > mean(U_draw)+0.5*std(U_draw)
% %                             jj2=jj2+1;
% %                             historiesH(jj2,:)=VAR_draw.X(ii,:);
% %                         end
% %                     end
% %                 end
%                     indexL  =[find(VAR_draw.X(:,c_case+ordend2)<=thrL2)]; indexL = setdiff(indexL,1);
%                     %             [VAR_draw.X(indexL,c_case+ordend2) repmat(thrL2,length(indexL),1)]
%                     indexLL = indexL(find(residStruct(indexL-1)<-0.5)); %< 25th perc
%                     indexLH = indexL(find(residStruct(indexL-1)> 0.5)); %> 75th perc
%                     historiesL = VAR_draw.X(indexLL,:);
%                     historiesH = VAR_draw.X(indexLH,:);
                %---------------------------------------------------------%
                %-------------- Replace Relevant code here BEG------------%
                %----------------------  UNEMPLOYMENT  -------------------%
%                THR = 6.5;
%               %THR = 0.0;
%                indexL  =[find(VAR_draw.X(:,c_case+ordend2)>THR)]; indexL = setdiff(indexL,1);
%                indexLL = indexL(find(residStruct(indexL-1,pick)<-0.5)); %< 25th perc
%                indexLH = indexL(find(residStruct(indexL-1,pick)> 0.5)); %> 75th perc
%                historiesL = VAR_draw.X(indexLL,:);
%                historiesH = VAR_draw.X(indexLH,:);
               %----------------------------------------------------------%
               %-------------- Replace Relevant code here BEG-------------%
               %----------------------------------------------------------%
               %--------------------------  PMI  -------------------------%
%                THR = 44.5;
%                indexL  =[find(VAR_draw.X(:,c_case+ordend2)<THR)]; indexL = setdiff(indexL,1);
%                indexLL = indexL(find(residStruct(indexL-1,pick)<-0.5)); %< 25th perc
%                indexLH = indexL(find(residStruct(indexL-1,pick)> 0.5)); %> 75th perc
%                historiesL = VAR_draw.X(indexLL,:);
%                historiesH = VAR_draw.X(indexLH,:);
                %---------------------------------------------------------%
                %-------------- Replace Relevant code here END------------%
                %---------------------------------------------------------%
                clear jj jj1 jj2 zz zz1 zz2
            else
                historiesL=zeros(1,VAR_draw.ntotcoeff);
                historiesH=zeros(1,VAR_draw.ntotcoeff);
                
            end
            
            [irf_drawL, irf_draw_optL] = VARirtrue_sim1shock_histories_futureN(VAR_draw,nsteps,pick,historiesL,ordend,ordend2,draws,mode,typeImpulse,fast);
            
            [irf_drawH, irf_draw_optH] = VARirtrue_sim1shock_histories_futureN(VAR_draw,nsteps,pick,historiesH,ordend,ordend2,draws,mode,typeImpulse,fast);
            
            if irf_draw_optL.nexplos~=length(historiesL) && irf_draw_optH.nexplos~=length(historiesH)
                IRFdraws_histL(:,:,:,tt)=irf_drawL;
                IRFdraws_histH(:,:,:,tt)=irf_drawH;
                tt = tt+1;
            else
                disp(['because of too large values of y_artificial repeat draw #: ' num2str(tt) ' (since all histories were discarded)' ]);
                numExpl=numExpl+1;
            end
            
            
            
            
        catch 
            disp(['because of too large values of y_artificial repeat draw #: ' num2str(tt) ' (for an error or warning in VARmodel f.)' ]);
            numExpl=numExpl+1;
        end
        
        warning ('on','all'); % restore warning state
        
        
    else 
        disp(['because esplosiveness(NaN) of y_artificial repeat draw #: ' num2str(tt)]);
        numExpl=numExpl+1;
    end
    
end


%% Compute the error bands
%=========================
%  using boostrap, use percentile (upper and lower bounds) bands type
% 1) CASE LOW PERCENTILE

INFavgL = zeros(nsteps,nvars,nvars);
SUPavgL = zeros(nsteps,nvars,nvars);
MEDavgL = zeros(nsteps,nvars,nvars);

pctg_inf =       (100-pctg)/2;
pctg_sup = 100 - (100-pctg)/2;
INFavgL(:,:,:) = prctile(IRFdraws_histL(:,:,:,:),pctg_inf,4);
SUPavgL(:,:,:) = prctile(IRFdraws_histL(:,:,:,:),pctg_sup,4);
MEDavgL(:,:,:) = prctile(IRFdraws_histL(:,:,:,:),50,4);

%%% 2) CASE HIGH PERCENTILE

INFavgH = zeros(nsteps,nvars,nvars);
SUPavgH = zeros(nsteps,nvars,nvars);
MEDavgH = zeros(nsteps,nvars,nvars);

%do a cycle here over histories TO GET BOOSTRAPPED GIRFS FOR EACH HISTORY

pctg_inf =       (100-pctg)/2;
pctg_sup = 100 - (100-pctg)/2;
INFavgH(:,:,:) = prctile(IRFdraws_histH(:,:,:,:),pctg_inf,4);
SUPavgH(:,:,:) = prctile(IRFdraws_histH(:,:,:,:),pctg_sup,4);
MEDavgH(:,:,:) = prctile(IRFdraws_histH(:,:,:,:),50,4);


disp('the percentage of draws repeated is of:')
percExpl=numExpl/ndraws
if percExpl>=0.25
    disp('Many discarded draws in the bootstrap. SUGGESTION: Start the sample in another date might help')
end
